2038
Inorg. Chem. 1984, 23, 2038-2043
continue to consider the relatively large AVNH> - AVc, differences as evidence for a predominantly dissociative mechanism. Acknowledgment. This research was supported by grants from the U S . National Science Foundation (P.C.F.) and from the Deutsche Forschungsgemeinschaft (R.v.E). Preliminary lifetime measurements in the nonaqueous solutions were carried out by Dr. Yves Ducommen while at UCSB on a Swiss National Science Foundation Postdoctoral Fellowship. J.D.
acknowledges the advice and help of V. C. Lamarca of the UCSB chemistry machine shop in modifying high-pressure emission cells. The pulse laser apparatus was purchased in part with funds from a U S . National Science Foundation Grant to the UCSB Quantum Institute. Registry No. FMA, 75-12-7; DMF, 68-12-2; Rh(NH3)Q2+, 15379-09-6; [Rh(NH3)4C12]CIO,, 67573-28-8; [Rh(NHp)SFMA](CIO,),, 90246-25-6; tram-[Rh(NHJ4(FMA)C1](CIO,),, 90246-26-7; Me2S0, 67-68-5; C1-, 16887-00-6;NH3, 7664-41-7.
Contribution from the Institute for Physical Chemistry, University of Frankfurt, 6000 Frankfurt/Main, FRG
Volume Profiles for the Base Hydrolysis of a Series of Pentaamminecobalt(II1) Complex Ions in Aqueous Solution' Y. KITAMURA,2R. VAN ELDIK,* and H. KELM Received October 6, 1983
Volumes of activation (APeXv,) for the base hydrolysis reactions of the complexes CO(NH~),X(~-")+, where X" = F,C1-, and Me2S0, were determined from the pressure dependencies of the hydrolysis rate constants and Br-, I-, NO3-, Sod2-, have values between 22 and 40 cm3mol-'. Partial molar volume measurem'entson all the reactant species, as well as overall reaction volume (AVO)determinations by a dilatometric technique, enable the construction of reaction volume profiles for the base hydrolysis reactions. These clearly demonstrate that AV(,prl - AVOis fairly constant for almost all the studied systems. Furthermore, these data enable the estimation of the partial molar volume of the five-coordinate species Co(NH3)4NH22+, which turns out to be independent of the nature of x". These results underline the validity of the SNICB mechanism and demonstrate the general applicability of volume equation calculations in obtaining information on the partial molar volumes of intermediate and/or transition-state species.
Introduction correlation between the partial molar volume of the complex and that of the neutral sixth ligand. Furthermore, he demOur general interest in the application of high-pressure onstrates very clearly that the calculated volume of the fivekinetic techniques in the elucidation of chemical reaction coordinate intermediate in the case of a dissociative mechanism mechanisms has led us to the study of typical aquation reacstrongly depends on the charge of the complex, i.e. the charge tions of ammine complexes of cobalt(III), rhodium(III), and of the sixth ligand-the leaving group during aquation. These chromium(III).3-9 Volume equation calculations were adopted and recent theoretical predictions by Swaddle13 clearly demto demonstrate that the aquation reactions of pentaammineonstrate that Stranks' postulate is indeed in error and another cobalt(II1) complexes proceed according to a dissociative reapproach must be sought. action mode.3 In these it was assumed that the partial molar volume of the five-coordinate transition state, C O ( N H ~ ) ~ ~ + , Along these lines we have studied the volume profiles for a series of base hydrolysis reactions of pentaa"inecobalt(II1) equals that of the hexaammine species on the basis of precomplexes. These are generally a~cepted'"'~to proceed acdictions presented by Stranks.lo In a later study Swaddle and cording to a SNICB mechanism in which a five-coordinate a co-worker' criticized this assumption and presented arguintermediate, CO(NH~)~NH?+, is formed, which rapidly reacts ments against a common five-coordinate intermediate and in with water or any other competing nucleophile to produce the favor of an Id mechanism. Furthermore, they also ascribed reaction products. If this is really the case, it should be possible the earlier found consistency in the partial molar volume of to estimate the volume of this common intermediate from the five-coordinate intermediate to errors in the partial molar reaction volume and volume of activation measurements. This volumes of some of the studied complexes. will add not only to the validity of the suggested mechanism Very recently, Lawrand* studied the pressure dependence but also to the general understanding of the applicability of of the aquation reactions of a series of pentaamminecobalt(II1) volume equation calculations and the construction of reaction complexes, all with neutral leaving groups. H e finds a good volume profiles.2s22 ~~
(1) A preliminary report was presented at the 21st EHPRG Conference, High Pressure in Chemistry and Biology, Copenhagen, Denmark, 1983; see Abstract No. 30. (2) On leave from the Dtpartment of Chemistry, Faculty of Science, Ehime University, Matsuyama, Ehime 790, Japan. (3) Palmer, D. A.; Kelm, H. Inorg. Chem. 1977, 16, 3139. (4) van Eldik, R.; Palmer, D. A.; Kelm, H. Inorg. Chem. 1979, 18, 1520. (5) Palmer, D. A. Ausr. J. Chem. 1979, 32, 2589. (6) Kitamura, Y.Bull. Chem. SOC.Jpn. 1977, 50, 2097. (7) K!tamura, Y.Bull. Chem. Soc. Jpn. 1979, 52, 3280. (8) Kitamura, Y.Bull. Chem. Soc. Jpn. 1982, 55, 3625. (9) Daffner, G.; Palmer, D. A.; Kelm, H. Inorg. Chim. Acta 1982, 61,57. (10) Stranks, D. R.Pure Appl. Chem. 1974, 38, 303. (11) Sisley, M. J.; Swaddle, T.W. Inorg. Chem. 1981, 20,2799. (12) Lawrance, G. Inorg. Chem. 1982, 21,3687.
(13) Swaddle, T.W.Inorg. Chem. 1983, 22. 2663. (14) Nordmeyer, F. R. Inorg. Chem. 1969, 8, 2780. (IS) Buckingham, D.A.; Olsen, I. I.; Sargeson, A. M . J. Am. Chem. SOC. 1967,89, 5129. (16) Buckingham, D. A.; Creaser, I. I.; Sargeaon, A. M. Inorg. Chem. 1970, 9, 655. (17) Jackson, W.G.; Sargeson, A. M. "Rearrangements in Ground and Excited States"; de Mayo, P.,Ed.; Academic Press: New York, 1980; Vol. 2, p 321. (18) Ahmed, E.;Tucker, M. L.; Tobe, M . L. Inorg. Chem. 1975, 14, 1. (19) Dixon, N. E.; Jackson, W. G.; Marty, W.; Sargeson, A. M. Inorg. Chem. 1982, 21,688. (20) van Eldik, R.; Kelm, H. Rev.Phys. Chem. Jpn. 1980, 50, 185.
0020-1669/84/1323-2038$01.50/0 0 1984 American Chemical Society
Base Hydrolysis of C O ( N H ~ ) ~ X ( ~ - " ) +
Inorganic Chemistry, Vol. 23, No. 14, 1984 2039
Experimental Section The following complexes were prepared as described in the literature; their chemical analysesz3were in excellent agreement with the theoretically expected values, and their UV-visible absorption spectra were in good agreement with those reported in the quoted references: [CO(NH~)~CI] (C104)z;z5926[Co(NH,),Br] (C104)z;263z7[Co[ C O ( N H ~ ) ~ N O ~ ] ( C ~ O[Co,)~;~~-~~ (NH3)SI](C104)z;26~z8 (NH~)~S04]C104~H~0;'9~30 [ C O ( N H ~ ) ~ O H ~ ] ( C ~[COO~)~;~*~~*~~ (NH3)SMezSO](C104)3~H20L9~32 [ C O ( N H ~ ) ~ F ] ( C(A~ O ~=) 51 ~ ~3 (c = 44.8) and 353 (c = 38.8) nm). Chemicals of analytical reagent grade and doubly distilled water were used throughout this study. UV-visible spectra were recorded on a Perkin-Elmer 555 spectroReaction coordinate photometer. pH measurements were performed with a Radiometer Figure 1. Volume profile for the overall reaction C O ( N H ~ ) ~ X ( ~ - ~ ) + pHM 64 instrument using a combination glass-reference electrode, + OH- C O ( N H ~ ) ~ O H+ ~X".+ of which the latter was filled with a saturated NaCl solution. Special care was taken to avoid the presence of CO, in the test solutions. For this reason the distilled water was boiled for several minutes and cooled eq 1 simplifies to koM = k2[OH-]. The linear dependence of under the exclusion of CO,. kow on [OH-] is a general characteristic of base-hydrolysis In the dilatometric studies a Carlsberg dilatometer was used and processes for such complexes and has been ascribed to the the procedures have been outlined elsewhere.33 The COz-freedistilled well-known and generally accepted SNICB mechanism:14-19 water was evacuated for a while before use. The commercially K obtained kerosene was purified by passing through a silica gel and CO(NH,),X(~-")+ OH- + an aluminum oxide column. The dilatometer was thermostated at 25.0 OC within an accuracy of f0.002OC. Approximately 25 min C O ( N H ~ ) ~ ( N H ~ ) X ( ~ -H " )2+0 was allowed for temperature equilibration before the complex solution k was mixed with the base (1:l). The extent of spontaneous aquation C O ( N H ~ ) ~ ( N H ~ ) X ( ~ - "C) +O ( N H ~ ) ~ N H ? + X" during this period was negligible. The percentage conversion was determined spectrophotometrically and was found to be 100%for X" fast C O ( N H ~ ) ~ N H ~H~2+0 C O ( N H ~ ) ~ O H (2) ~+ = C1-, Br-, I-, NO3-, and MezSO. Kinetic measurements were performed on a Zeiss PMQ I1 specUnder pseudo-first-order conditions, i.e. at least a 10-fold trophotometer equipped with a thermostated (k0.1"C) high-pressure excess of OHce113433sand on a high-pressure stopped-flow in~trument.~~ The hydrolysis reactions were studied under pseudo-first-order conditions, kobsd = kK[OH-]/(l K[OH-1) (3) and the observed rate constants, koM, were calculated in the usual way. The corresponding first-order plots were linear for at least 3 which in general simplifies to kobd = kK[OH-1, since 1 + half-lives of the reaction when the experimentally obtained infinity absorbance was employed. Only in the case of the C O ( N H ~ ) ~ F ~ +K[OH-] = 1 due to the magnitude of K.38 It follows that the observed second-order rate constant k, is a composite quantity, species was the Guggenheim method adopted over the first half-life, viz. k2 = kK, where K is the equilibrium constant for the since decomposition of the complex occurred during the later stage deprotonation of the amine and k the rate constant for the of the base hydrolysis process. The apparent molar volumes of the investigated complexes were formation of the five-coordinate intermediate. measured with a digital densimeter, Anton Paar DMA 02, which was The base hydrolysis reactions investigated in this study are thermostated at 25.000 i 0.002 "C. A range of concentrations (5-15 such that k2[OH-] >> k,. This tendency can clearly be seen mM) was studied for each complex, and the apparent molar volumes from a comparison of the rate data in Table I with those were averaged since they showed no significant concentration depublished elsewhere for the spontaneous aquation processpendence. es.30,37,39The values of k2 at ambient pressure are in good
-
+
+ -
+
+
+
Results and Discussion The aquation reactions of complexes of the type Co(NH3)sX(3-")+are in general catalyzed by base, such that
agreement with literature data especially when the difference in ionic strength is taken into a c c o ~ n t . ~ ~ * ~ ~ ~ ~ The base hydrolysis of C O ( N H ~ ) ~ was C ~ ~studied + at different ionic strengths (see Table I) and under similar conditions (p = 10 mM) at two different occasions to determine the kobd = kl + k2[OH-] (1) reproducibility of the measurements. Plots of In kobsdvs. where kl is the rate constant for spontaneous aquation and pressure are linear within the experimental error limits for all k2 is that for the base-catalyzed path. At higher [OH-] the the studied systems up to 1 kbar. The volumes of activation k2 path overrules the spontaneous aquation p r o c e ~ s and ~ ~ ~ ~ ' are obtained from eq 4, where yA,yB,and y * are the activity Palmer, D. A,; Kelm, H. Coord. Chem. Rev. 1981, 36, 89. Merbach, A. E. Pure Appl. Chem. 1982, 54, 1479. Spiro, T. G.; Revesz, A.; Lee, J. J . Am. Chem. SOC.1968, 90, 4000. Basolo, F.; Murmann, R. K. Inorg. Synrh. 1953, 4, 172. Schlessinger, G. G. Inorg. Synth. 1967, 9, 160. Buckingham, D. A.; Olsen, I. I.; Sargeson, A. M. J . Am. Chem. SOC. 1966,88,5443. Diehl, H.; Clark, H.; Willard, H. H. Inorg. Synth. 1939, 1 , 186. Yalman, R. G. J . Am. Chem. SOC.1955, 77, 3219. Swaddle, T. W. J . Am. Chem. SOC.1967,89, 4338. Jones, W. E.; Carey, L. R.; Swaddle, T. W. Can. J. Chem. 1972, 50, 2739. van Eldik, R.; Harris, G. M. Inorg. Chem. 1975, 14, 10. Mac-Coll, C. R. P.; Beyer, L. Inorg. Chem. 1973, 12, 7. Kitamura, Y. Bull. Chem. SOC.Jpn. 1979, 52, 3453. Fleischmann, F. K.; Conze, E. G.; Stranks, D. R.; Kelm, H. Rev. Sci. Instrum. 1974.45, 1427. le Noble, W. J.; Schlott, R. Rev.Sci. Instrum. 1976, 47, 770. van Eldik, R.; Palmer, D. A.; Schmidt, R.; Kelm, H. Inorg. Chim. Acta 1981, 50, 131.
coefficients for the C O ( N H ~ ) ~ X ( ~species, - " ) + the hydroxy ion, and the activated complex, respectively. The first term in eq 4 was determined from the slope of the In k2 (or In kOM)vs. pressure plot, for which it was assumed that [OH-] is independent of pressure$l The second term (AV,) was estimated by using the Debye-Hiickel limiting law for the activity (37) Buckingham, D. A.; Marty, W.; Sargeson, A. M. Inorg. Chem. 1974, 13, 2165. (38) Tobe, M. L. 'Inorganic Reaction Mechanisms"; Thomas Nelson: London, 1972, p 94. (39) House, D. A. Coord. Chem. Rev. 1977, 23, 223. (40) Davies, M. B.; Lalor, G . C. J . Inorg. Nucl. Chem. 1969, 31, 2189. (41) Hamann, S. D.; le Noble, W. J. J . Chem. Educ., in press.
Kitamura, van Eldik, and Kelm
2040 Inorganic Chemistry, Vol. 23, No. 14, 1984
Table I. Values of kobsd for the Base Hydrolysis of a Series of Pentaamminecobalt(II1) Complexes as a Function of Pressure at 25 "C
complex Co( NH ,) F2+
Co(NH,),C12+
Co(NH,), BrZ+
ionic [complex], [OH-], wavelength, strength, mM mM nm mM 0.36
10
244
11
0.07
1
24 0
1
0.07
1
240
100
0.07
1
240
1oa
0.07
1
240
1ooa
10
290
13
1
pressure, bar 12.0 9.20 7.12 5.89 4.18 3.24 2.78
12.7 10.0 6.57 5.46 4.45 3.64 2.63
8 253 507 760 1013 1266 1520 8 25 3 507 760 1013 1266 1520 8 253 507 760 1013 1266 1520 8 253 507 760 1013 1266 1520
11.3 8.00 5.69 4.05 2.90 2.33 1.77 8.45 5.59 3.92 2.84 2.24 1.62 1.49 8.90 6.03 4.49 3.18 2.36 1.83 1.38 4.62 3.05 2.27 1.62 1.23 0.96 0.81
10.9 8.64 5.83 4.06 2.94 2.16 1.76 8.30 5.68 3.13 2.84 2.30 1.79 1.43 8.51 6.15 4.30 2.96 2.36 1.76 1.40 4.60 3.21 2.23 1.61 1.30 1.01 0.84
20
3.39 3.70 3.02 3.05 1.68 1.69 1.25 1.28 1.17 1.06
3.21 3.84 3.00 2.93 1.60 1.69 1.30 1.35 1.10 1.09
3.53 3.58 3.05 2.89 1.64 1.69 1.24 1.39 1.09 1.08
2
7.60 8.09 7.06 6.87 4.52 4.35 2.96 2.92 2.39 2.27
7.63 8.22 6.92 6.83 4.62 4.35 2.88 2.98 2.5 1 2.32
7.63 8.16 7.00 6.81 4.53 4.21 2.97 3.00 2.42 2.24
2
2.55 2.42 1.82 1.93 1.61 1.56 1.09 1.07 0.705 0.725
2.45 2.35 1.87 2.00 1.57 1.48 1.11 1.07 0.733 0.715
2.4 1 2.42 1.89 2.05 1.53 1.47 1.11 1.03 0.722 0.710
1
500 750 1000 0.2
10
310
11
20 250 500 75 0 1000
Co(NH,), NO, '+
1
10
290
13
20 250 500 750 1000
Co(NH,),SO,+
0.36
10
260
10
- x
8 253 507 760 1013 1266 1520
250
Co(NH,), 12+
10Xkobs& s-'
8 253 507 760 1013 1266 1520
10.4 8.20 6.35 5.22 4.27 3.25 2.85
10.3 8.67 6.55 5.14 4.35 3.38 2.76
5 9.22
4
4
4
4
4 7.90
Base Hydrolysis of C O ( N H ~ ) ~ X ( ~ - ~ ) +
Inorganic Chemistry, Vol. 23, No. 14, 1984 2041
Table I (Continued) ionic [complex], mM
-complex
[OH-], wavelength, strength, mM
nm
mM
pressure, bar
10
400
16
20
1 0 x k & d , s-'
X ~
1
Co(NH,) ,Me, SO3'
250 500 750
1000
3.48 3.76 2.69 2.65 1.87 1.86 1.17 1.21 0.801 0.763
3.51 3.75 2.66 2.61 1.88 1.84 1.18 1.20 0.792 0.770
3.55 3.83 2.68 2.61 1.86 1.85 1.22 1.16 0.782 0.767
3.55
1
0.781
By addition of NaC10,.
coefficients and taking the pressure dependence of the water density and its dielectric constant into a c c ~ u n t . ~ The ~,~~ magnitude of A V 7 (cm3 mol-') turns out to be as follows: 0.6 (X" = F,C1-, Br-, NO3-, I- a t ionic strength 10-13 mM); 0.2 (X" = C1- at ionic strength 1 mM); 0.3 (X" = S042-at ionic strength 10 mM); 1.8 X" = C1- at ionic strength 100 mM); 1.1 (X" = Me2S0 at ionic strength 16 mM). The resulting values of AVcxptlare summarized in Table 11. The values of AV,, are large and positive in all cases and a composite of the contributions of the effect of pressure on k and K according to eq 5 . This is illustrated in the general
AVcxptl = A P ( Q
+ AV(k)
(5)
volume profile for such base hydrolysis reactions in Figure 1. The values of AV,, for the chloro and bromo complexes are in close agreement with the respective values 33.4 and 32 cm3 mol-' reported before.6.44 Furthermore, it is important to note that these values in Table I1 are subjected to relatively small error limits and do not show any appreciable ionic strength dependence. According to the volume profile in Figure 1, it is expected that AV, and ATo (the overall reaction volume) should depend on the nature of Xp, i.e. especially on the charge and size of the leaving group. This is clearly seen in the values of AVcxMfor X" = Me2S0, C1-, and Sot-. The difference AVexptl- AVO,however, should be independent of the nature of X" since it only involves the recombination of Co(NH3)4NH?+ and H 2 0 to produce C O ( N H ~ ) ~ O HIn ~ +order . to investigate the validity of this statement, A P for the overall base hydrolysis process was (a) measured dilatometrically and (b) calculated from partial molar volume measurements. The ATo values in Table I1 were determined with a Carlsberg dilatometer, except for the fluoro complex, where unreproducible results were obtained due to the subsequent decomposition of the complex. The quoted results are the average of two or more determinations and were corrected for changes in ionic strength during the mixing of the reactant solution^.^^^^^ The ionic strength dependence of the apparent molar volume (4i)of an ionic species is approximated by eq 6 , where is the apparent molar volume at infinite dilution
& = di,-, + 0.93zi2p1/2
(6)
and q the charge on the ion. The reaction volume at infinite dilution was obtained from eq 7, where Arm, has the values AVO = AKexptl- AFmr
(7)
(42) Grindley, T.; Lind, J. E. J. Chem. Phys. 1971, 54, 3983. (43) Srinivasan, K. R.; Kay, R. L. J. Chem. Phys. 1974, 60, 3645. (44) Okubo, T.; Maruno, T.; Ise, N. Proc. R. Soc. London, Ser. A 1980,370, 501. (45) Redlich, 0.;Meyer, D. M. Chem. Reu. 1964, 64, 221. (46) Millero, F. J. "Water and Aqueous Solutions: Structure, Thermody-
namics and Transport Processes"; Home,R. A., Ed.;Wdey-Interscience: London, 1972; Chapter 13.
0 (X" = F,C1-, Br-, I-, NO3-), 1.3 (X" = S042-),and -1.8 cm3mol-' (X" = Me8O). The values of AVO(Table 11) show a strong dependence on the nature of X"; the largest value is for the leaving of a neutral molecule (Me2SO) and the smallest value (even negative!) for the leaving of a highly charged species (Sot-).These tendencies emphasize the important role played by electrostriction in base hydrolysis reactions. The AVOvalues in Table I1 are in good agreement with those estimated from partial molar volume data for educt and product species as shown in Tables I11 and IV, which were either obtained from density measurements or taken from the literature. The adopted partial molar volumes call for some comments since significant discrepancies have been Our value for [CO(NH~)~CI](C~O~), is in close agreement with other ~ a l u e s ~but a ' ~differs significantly from the value reported by Sisley and Swaddle." We do not understand this discrepancy since their compound gave in our laboratory'' a value of 180 f 2 cm3 mol-', which is in close agreement with the present results. We cannot go along with the explanation that the difference may be due to a difference in humidity.' The ATmlcdvalue for the hydrolysis of the sulfato complex is in excellent agreement with the AVOvalue and further underlines the large collapse in volume due to significant charge creation during the release of SO4". Spiro et al.23reported a value of +1.4 cm3 mol-' for this reaction at 30 OC. However, they made a trivial error in the calculation of APmr,such that a value of -1.5 cm3 mol-' in fact arises from their data, which is fairly close to ours. Their23results for the chloro, bromo, and nitrato complexes are close to those found in this study. A remarkable observation in Table I1 is the fact that AV& - ATo is indeed fairly constant for all the complexes, except the sulfato species, which has a significantly larger value. The remainder of the complexes show an average vlaue of 19.7 f 2.1 cm3 mol-'. This volume decrease (see Figure 1) almost equals the partial molar volume of water, demonstrating that a water molecule is completely absorbed during the final step of the base hydrolysis process. Alternatively, this volume decrease is very close to that found for the ionization of water at 25 OC, viz. -22.1 cm3 m01-1,47948suggesting that the addition of water to the five-coordinate intermediate proceeds via the protonation of the amide ligand and subsequent addition of hydroxide or vice versa. In addition, as will be seen later, the partial molar volumes of C O ( N H ~ ) ~ N Hand ~ ~ +Co(NH3)50H2+are indeed very similar, from which is follows that a water molecule is inserted into the coordination sphere of C O ( N H ~ ) ~ N H ?without + a remarkable increase in volume of the latter species. Although the most of the data in Table I1 are for 2+ charged complexes, the value of AVexpt,- AVO for the Me2S0 complex falls well within the range of values (47) Kitamura, Y.; van Eldik, R. Ber. Bunsenges. Phys. Chem. 1984,88,418. (48) Millero, F.J.; Hoff, E. V.;Cahn, L. J. Solution Chem. 1972, I , 309.
Kitamura, van Eldik, and Kelm
2042 Inorganic Chemistry, Vol. 23, No. 14, 1984 Scheme I
Table 11. Activation and Reaction Volumes for a Series of Base Hydrolysis Reactions of the Typea CO(NH,),X(~-")++ OH- -+ Co(NH,),OH" + X"-
+
C O ( N H ~ ) ~ X ( ~ - ~ )ow +
e C O ( N H ~ ) ~ ( N H , ) X ( ~ - ~ +) +
RHX
ionic
RX
+
:c~(NH~I,(NH,)~+
FCI -
Br' 1-
NO,S0,Z' Me,SO
11 1 10 10 100 13 11 13 10 16
26.4 33.6 33.0 33.0 33.8 32.5 33.6 31.0 22.2 40.2
1.0 t 0.6 2 0.8 t 1.4 f 1.0 i 1.4 t 1.0 t 0.8 t 0.7 t 0.5
7.4
t
l.Od
19.0 t 2.0
9.9
t
0.2
23.1
t
1.0
11.1 15.5 13.2 -3.9 21.2
i
0.2 0.3 0.4 0.4 0.3
21.4 t 18.1 t 17.8 t 26.1 t 19.0 t
1.6 1.3 1.2 1.1 0.8
t
z
VR
VH20 -
+ Vx +
VRHX- VOH VHzo - VRHX - VoH
(8)
-E" 140
+ xn- +
HO ,
fori- CO(NH~)~OH*++ xnRHOH
~
E
-
l>":
120-
d "
-
20
Figure 2. Plot of Apcxptl+ and IV.
Slope : 0 9 0 i 0 0 9 Intercept = 92 0 i 3 4
-
60
80
LO
Vx,
cm3
mol-'
rRHxvs. Vx from the data in Tables I1
+
that V* z VR Fx. The only unknown in eq 8 is VR,and its values are summarized in Table IV. It is seen that VR is remarkably constant, especially when the various approximations and error limits are taken into account. Furthermore, no significant dependence on the nature of X" exists, underlining the principle of a common intermediate in all cases. Alternatively, eq 8 can be rewritten in the form given by eq 10, from which it follows that a plot of AVSexptl+ VRHX
AV
(9)
eq 8 it is assumed that the dissociative reaction of the conjugate base species RX has a late ("productlike") transition state, such
-
160
f
AVexpti = V* +
HO ,
R
Temperature = 25 "C; all volume quantities in em3 mol-'. Calculated from the data in Table I with use of eq 4. Measured with a Carlsberg dilatometer-see Results and Discussion. Estimated from molar volume measurements-see Table IV.
found for the 2+ species. The deviation in the case of the sulfato complex can probably be ascribed to the occurrence of ion-pair formation between CO(NH~)~NH;+ and SO4*-in the transition state. This would mean that AVS,,,, - AVOdoes represent not only the entrance of a water molecule but also the dissociation of the ion pair if it is assumed that the final product species exist as individual ions in solution. This effect should be significantly smaller for singly charged and neutral leaving groups. Another aim of this study was to obtain more information on the partial molar volume of the C O ( N H ~ ) ~ N Hinter~*+ mediate species. If we rewrite the overall reaction system in the way indicated in Scheme I, i.e. a combination of the reactions in (2) and Figure 1, eq 8 and 9 can be formulated. In
+
R CO(NH,),(NH,?+
t t t t
xn-i+
i
HO ,
+ VRHX= i;k + r1.1~0 - 70~ + Vx
(10)
vs. Vx should be linear with a slope of unity and an intercept VR VH20- POOH, i.e. VR 17.6.46*49 Such a plot is given
+
+
Table 111. Apparent Molar Volumes (em3 mol-') of Some Co(II1) Ammine Complexes at 25 "C
a
complex
ref 3
ref 11
ref 12
[Co(NH,), Fl (CIO,), lCo(NH,),CIl (C10,) [Co(NHJ,Brl(CIO,), [Co(NH,),I] (C10,)z [ Co(NH3) 5 NO, 1 (C1O,), [ Co(NH,) ,SO, ]C10, [Co(NH,) ,Me,SOl (CIO,),
159.3 t 0.4 187.2 i: 0.4 196.4 f 1.1
168.8 184.6
179.0
Value for [Co(NH,),NO,](NO,),.
161.1 2 l . l a 147.2 t 0.6 277.3 t 1.4
137.7 253.8
this work 160.8 t 1.0 180.7 t 0.2 185.7 t 2.1 192.0 t 0.8 182.6 t 0.8 143.2 t l . l b 258.0 t 0.9b
Corrected for 1 mol of water of crystallization.
Table IV. Molar Volume Data and Volume Equation Calculations for the Series of Base Hydrolysis Reactionsa CO(NH,),X("~)+ + OH' Co(NH,),0H2* + X"complex @lb VRHX' 7Xd Avcalcde AVof VRg [Co(NH,),Fl(ClO,)z 160.8 t 1.0 63.6 t 1.0 3.3 7.4 i 1.0 69.1 i: 2.0 [Co(NH 3 ) 5 Cll (C10 4 ) 2 180.7 t 0.2 83.5 t 0.2 22.3 6.5 t 0.2 9.9 t 0.2 76.6 t 1.0 [Co(NH,) ,Br1 (C10, I z 185.7 t 2.1 88.5 t 2.1 29.2 8.4 i: 2.1 11.1 t 0.2 74.2 t 3.5 [Co(NH,),Il(ClO,), 192.0 t 0.8 94.8 t 0.8 40.7 13.6 * 0.8 15.5 0.3 70.1 t 1.8 [Co(NH,), NO,] (ClO,), 182.6 i 0.8 85.4 * 0.8 33.5 15.8 t 0.8 13.2 * 0.4 65.3 t 1.6 I W N H ,) SO, 1C10 143.2 t 1.1 94.6 t 1.1 23.0 -3.9 t 1.1 -3.9 t 0.4 76.2 t 1.8 [CoWH,), Me,SO] (ClO,), 258.0 t 0.9 112.2 t 0.9 68.8h 24.3 t 0.9 21.2 t 0.3 66.0 t 1.4 av 71.1 i: 3.9
--f
Temperature = 25°C; all volume quantities in cm3 mol-'. Apparent molar volume, from densit4Lmeasurements-see Table 111. Estimated by using V(C10,') =48.6 (see footnoted). Taken from ref 46 on the assumption that V(H') =-4.5. e Calculated by using eq 9, and OH = 0.5 (see footnote d ) and ~ R ~ = O 68.2 H (volume of neutralization of CO(NH,),OH,~+is 25.54' and T ( C O ( N H , ) , O H ~ ~=+ ) 60.3 (footnote c and ref 3)). Data reported In Table 11. Calculated by using eq 8, and &H = 0.5 (see footnote 6)and ~ H , O = 18.1. Taken from ref 3. a
Inorganic Chemistry, Vol. 23, No. 14, 1984 2043
Base Hydrolysis of C O ( N H ~ ) ~ X ( ~ - " ) + Table V. Values of A'i;cK) and AV'(k) for the Series of Base Hydrolysis Reactions at 25 "C? CO(NH,),X(~-")' + OH-
K
CO(NH,),(NH,)X('-")+ t H,O
.i
Co(NH,),NH," X"'
AViexptib
FCI Br INO,-
26.4 33.0 32.5 33.6 31.0 22.2 40.2
so,'-
Me,SO
Az~ -3 -3 -3 -3 -3 -1 -5
+ X"'
AV(K)'
AV*(kld
22.0 22.0 22 .o 22.0 22.0 17.0 27.0
4.4 11.0 10.5 11.6 9 .O 5.2 13.2
All volume data in cm3 mol-'. From Table 11. Estimated by using eq 5 . by using eq 1 1 .
Estimated
in Figure 2, which demonstrates that the data satisfy eq 10. The value of P,, viz. 74.4 f 3.4 cm3 mol-', is in good agreement with that calculated above (see Table IV). The magnitude of PRin Table IV is close to the value of 68.2 cm3 mol-' estimated45for the C O ( N H ~ ) ~ O H species, ~ + from which the conclusion could be drawn that these five- and six-coordinated Co(II1) complexes have approximately the same v ~ l u m e . ~ It , ' ~is, however, important to note that this agreement is probably only due to the fact that the partial molar volume of OH- is almost zero. It has been shown that P for such Co(II1) complexes depends linearly on the volume of the sixth ligand coordinated to the C O ( N H ~ ) moiety.12 ~~+ Furthermore, the value of PRis significantly larger than P for C O ( N H ~ ) ~ O H ?(60.3 + cm3 mol-')I2 and C O ( N H ~ ) (61.3 ~~+ cm3 m0l-').~9" This difference can be explained to result from differences in electrostriction, since our recent measurements4' demonstrated that 3+ complex ions can be ca. 12.5 cm3mol-' smaller than 2+ complex ions of similar nature. To sum up, the volume equation calculations performed above do not only underline the general validity of the suggested mechanism but also provide direct information regarding the volume of a five-coordinatespecies. The fact that PRdiffers significantly from that for closely related 3+ charged complexes but that it agrees well with the value for Co(NH&OH2+ is an important conclusion and should simplify the handling of such species in future investigations. (49) 'Handbook of Chemistry and Physics", 47th ed.;Chemical Rubber Publishing Co.: Cleveland, OH, 1967; p F-4.
We now turn to a discussion of the values of AVexptlreported in Table 11. The composite nature of this quantity has been referred to above (Figure 1 and eq 5). We are interested in obtaining values for AV+(k) since that should provide more information on the nature of the dissociative process. A reasonable estimate of AP(K) is needed, since this cannot be determined experimentally in the usual way due to the magnitude of K. We, therefore, measured the volumes of neutralization for a series of aquo and ammine complexes that have pK, values in the range 2.7-10.9.4' These complexes were considered to be model systems to deduce the influence of charge on the magnitude of AP(K). The results demonstrated the close similarity between aquo and ammine complexes, and the volumes of neutralization could be expressed as shown in eq 11, where Az2 is the difference in the squares of the charges AP(K) = (14.5 f 0.8) - (2.5 f O.2)Az2 (11) on the deprotonated and protonated complex species, respectively. With the aid of this relationship, AP(K) was estimated for the formation of the various conjugate base species and AV(k) could be calculated as shown in Table V. The values of AhVs(k) are almost similar for the chloro, bromo, iodo, and nitrato complexes. This is reasonable since these reactions involve the dissociation of ions of similar charge and approximately the same volume (see Table IV). The values for the fluoro and sulfato complexes are significantly smaller, illustrating the effect of electrostriction during this reaction especially in the case of the sulfate species. The partial molar volume of fluoride is indeed very small (Table IV) and indicates that the fluoride ion is a dense charge point. This, through electrostriction or the absolute size of the fluoride ion, can account for the small AVl(k) value for the fluoro complex. Finally, the largest value of AV(k) is for the Me2S0 complex, in line with bond breakage and no significant changes in electrostriction. It follows that A V ( k ) strongly depends on the nature of the leaving group as expected for a dissociative reaction process. Acknowledgments. The authors gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft, Fonds der Chemischen Industrie, and the Max Buchner Forschungsstiftung. Y.K. wishes to thank Ehime University for sabbatical leave, the University of Frankfurt for a visiting professorship, and Ryuichi Kume, a graduate student at Ehime University, for the preparation of some of the complexes used in this study. Registry No. Co(NH&NH?+, 90219-23-1; C O ( N H ~ ) ~ F ~ + , 15392-06-0; C O ( N H ~ ) ~ C14970-14-0; ~~+, C O ( N H , ) ~ B ~ 14970~ + , 15- 1 ; Co(NH3)5I2+, 15392-08-2; C O ( N H ~ ) S ( N O ~ ) ~15077-47-1; +, CO(NH3)s(S0,)+, 18661-07-9; C O ( N H ~ ) ~ ( M ~ ~ S 4491 O ) ~ 5-85-7. +,
